Analytic understanding of diffusion models

Diffusion models achieve state-of-the-art performance in generative modeling, yet their theoretical foundations and generalization behavior remain poorly understood. This tutorial focuses on the analytical understanding of diffusion models, addressing the apparent paradox between closed-form optimal denoisers and the empirical success of deep diffusion networks. It introduces recent theoretical advances that explain how mechanisms such as score smoothing, training dynamics, neural network inductive biases, and data structure contribute to generalization. By combining mathematical insights with hands-on experiments, the tutorial provides a principled framework for understanding the inner workings of diffusion models and for interpreting recent developments in the field.